Brinell Hardness Number Calculator

Enter the test load and the diameters of the ball indenter and the resulting indentation to compute the Brinell Hardness Number (HB) using the standard HB = 2P / [πD(D − √(D² − d²))] formula.

Quick Facts

Formula
HB = 2P / [πD(D − √(D² − d²))]
P is the load in kgf; D is the ball diameter and d the indentation diameter, both in mm. ASTM E10 / ISO 6506 recommend keeping d/D between 0.24 and 0.6 for a valid reading.

Results

Calculated
Brinell Hardness (HB)
—
HB = 2P / [πD(D − √(D²−d²))]
Indentation depth (h)
—
h = (D − √(D²−d²)) / 2
Indentation surface area (A)
—
Curved cap area; HB = P / A
d / D ratio
—
ASTM E10 valid range: 0.24–0.6

How to use this calculator

Enter the test load (P) applied through the ball indenter, in kilograms-force, then enter the ball diameter (D) and the indentation diameter (d), both in millimeters. Click Calculate to get the Brinell Hardness Number. Click Clear to reset all fields to the example values.

The Brinell hardness formula

The Brinell hardness test presses a hardened steel or tungsten carbide ball into a material's surface under a fixed load, then measures the diameter of the round indentation left behind. The Brinell Hardness Number is calculated as:

HB = 2P / [πD(D − √(D² − d²))]

where P is the test load in kilograms-force (kgf), D is the diameter of the ball indenter in millimeters, and d is the diameter of the indentation in millimeters. This is equivalent to HB = P / A, where A is the curved surface area of the spherical-cap indentation, so a harder material (smaller indentation for the same load) produces a larger HB. HB is conventionally reported as a bare number, or written with the ball and load, for example "235 HBW 10/3000" for a 10 mm tungsten carbide ball under 3000 kgf.

Understanding the inputs

Standard Brinell tests commonly use a 10 mm ball with a 3000 kgf load for steel and other hard metals, or 1500 kgf and 500 kgf loads for softer metals like aluminum and copper alloys. Smaller balls (5, 2.5, 2, or 1 mm) are used for thinner samples or smaller test areas, scaled with a proportionally lower load to keep the d/D ratio in range. The indentation diameter is measured with a low-power microscope or optical scale after the ball is removed.

Interpreting the results

The Brinell Hardness card is the primary result. The Indentation depth card shows how deep the ball sank into the surface. The Indentation surface area card is the curved contact area the formula divides the load by (HB = P / A). The d / D ratio card checks the indentation against the ASTM E10 / ISO 6506 recommended range of 0.24 to 0.6 — a ratio outside that range means the test load or ball size should be adjusted for a more reliable reading.

Frequently Asked Questions

What is the Brinell hardness formula?
HB = 2P / [πD(D − √(D²−d²))], where P is the test load in kilograms-force (kgf), D is the diameter of the hardened ball indenter in millimeters, and d is the diameter of the resulting round indentation, also in millimeters. The result is conventionally reported as a bare number, or in kgf/mm².
Why does the d/D ratio matter?
ASTM E10 and ISO 6506 recommend keeping the indentation-to-ball diameter ratio (d/D) between 0.24 and 0.6. Too shallow an indentation is hard to measure accurately, while too deep an indentation distorts the ball or exceeds the material's uniform-stress zone. Both extremes reduce the accuracy of the hardness reading.
What do HBW and HBS mean?
The letter after HB records the indenter material: HBW means a tungsten carbide ball was used, and HBS means a hardened steel ball. A full result is often written with the ball diameter and load, for example 235 HBW 10/3000, meaning a 235 hardness number measured with a 10 mm tungsten carbide ball under 3000 kgf.
How does Brinell hardness compare to Vickers or Rockwell?
All three tests press an indenter into a surface and relate load to indentation size, but they use different indenter shapes, loads, and formulas, so the numbers are not directly interchangeable. Brinell's large ball and indentation make it well suited to coarse-grained or non-uniform materials like castings, where it averages out local variations better than the smaller Vickers or Rockwell indenters.